Separation Logic for Small-Step cminor

Abstract

cminor is a mid-level imperative programming language; there are proved-correct optimizing compilers from C to cminor and from cminor to machine language. We have redesigned cminor so that it is suitable for Hoare Logic reasoning and we have designed a Separation Logic for cminor. In this paper, we give a small-step semantics (instead of the big-step of the proved-correct compiler) that is motivated by the need to support future concurrent extensions. We detail a machine-checked proof of soundness of our Separation Logic. This is the first large-scale machine-checked proof of a Separation Logic w.r.t. a small-step semantics. The work presented in this paper has been carried out in the Coq proof assistant. It is a first step towards an environment in which concurrent cminor programs can be verified using Separation Logic and also compiled by a proved-correct compiler with formal end-to-end correctness guarantees.